Computer_Vision/Chapter01/Back_propagation.ipynb

import numpy as np 
from copy import deepcopy
import matplotlib.pyplot as plt
x = np.array([[1,1]])
y = np.array([[0]])

from copy import deepcopy
import numpy as np
def feed_forward(inputs, outputs, weights):     
    pre_hidden = np.dot(inputs,weights[0])+ weights[1]
    hidden = 1/(1+np.exp(-pre_hidden))
    out = np.dot(hidden, weights[2]) + weights[3]
    mean_squared_error = np.mean(np.square(out - outputs))
    return mean_squared_error

def update_weights(inputs, outputs, weights, lr):
    original_weights = deepcopy(weights)
    temp_weights = deepcopy(weights)
    updated_weights = deepcopy(weights)
    original_loss = feed_forward(inputs, outputs, original_weights)
    for i, layer in enumerate(original_weights):
        for index, weight in np.ndenumerate(layer):
            temp_weights = deepcopy(weights)
            temp_weights[i][index] += 0.0001
            _loss_plus = feed_forward(inputs, outputs, temp_weights)
            grad = (_loss_plus - original_loss)/(0.0001)
            updated_weights[i][index] -= grad*lr
    return updated_weights, original_loss

W = [
    np.array([[-0.0053, 0.3793],
              [-0.5820, -0.5204],
              [-0.2723, 0.1896]], dtype=np.float32).T, 
    np.array([-0.0140, 0.5607, -0.0628], dtype=np.float32), 
    np.array([[ 0.1528, -0.1745, -0.1135]], dtype=np.float32).T, 
    np.array([-0.5516], dtype=np.float32)
]

losses = []
for epoch in range(100):
    W, loss = update_weights(x,y,W,0.01)
    losses.append(loss)
plt.plot(losses)
plt.title('Loss over increasing number of epochs')

Text(0.5, 1.0, 'Loss over increasing number of epochs')

W

[array([[ 0.01424004, -0.5907864 , -0.27549535],
        [ 0.39883757, -0.52918637,  0.18640439]], dtype=float32),
 array([ 0.00554004,  0.5519136 , -0.06599568], dtype=float32),
 array([[ 0.3475135 ],
        [-0.05529078],
        [ 0.03760847]], dtype=float32),
 array([-0.22443289], dtype=float32)]

pre_hidden = np.dot(x,W[0]) + W[1]
hidden = 1/(1+np.exp(-pre_hidden))
out = np.dot(hidden, W[2]) + W[3]

out

array([[-0.0174781]])